The present invention relates to n-valued Linear Feedback Shift Registers (LFSRs). More specifically it relates to equivalency of n-valued LFSRs in Fibonacci and Galois configuration.
Data scramblers, descramblers, sequence generators, detectors and coders based on shift registers with feedback are important components in data communications and data transfer in applications such as magnetic and optical data storage. It is known that linear feedback shift registers (LFSRs) can be realized in Fibonacci and Galois configurations. LFSRs in Fibonacci configuration are easier to analyze. Descramblers in Fibonacci are self-synchronizing. No prior art was found with sequence descramblers in a first Galois configuration. However descramblers in a first Galois configuration herein provided as an aspect of the present invention are not self-synchronizing. LFSRs in Galois configuration require fewer clock cycles for execution than Fibonacci equivalents.
LFSRs are also of interest in n-valued applications with n>2. It is sometimes advantageous to design an LFSR in Fibonacci configuration, while implementing it in Galois configuration. It may also be advantageous to implement an n-valued sequence generator in Galois configuration, because it is fast. One may want also to create a matching self synchronizing detector for such a generator, which may be in Fibonacci configuration. The rules for creating corresponding n-valued Fibonacci equivalent LFSRs in descramblers to Galois scramblers were not known prior to the present invention.
Accordingly methods for designing corresponding Galois and Fibonacci LFSRs and self-synchronizing descramblers in Galois configuration are required and apparatus implementing corresponding Galois and Fibonacci devices are required.